solve a system with matrix inverses or augmented matrices

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Zee writes the system 3y + 2x = 8 and x − 4y = 1 as AX = B. Which matrix equation is it?

   • [3, 2; 1, -4][x; y] = [8; 1]
   • [2, 3; 1, 4][x; y] = [8; 1]
   • [2, 3; 1, -4][x; y] = [8; 1]
   • [2, 1; 3, -4][x; y] = [8; 1]
   • [2, 3; 1, -4][8; 1] = [x; y]
2. 2.

   Esme writes the system 5x − 2y = 3 and 4y + x = 9 as AX = B. Which matrix equation is it?

   • [5, 1; -2, 4][x; y] = [3; 9]
   • [5, -2; 1, 4][3; 9] = [x; y]
   • [5, -2; 1, 4][x; y] = [3; 9]
   • [5, 2; 1, 4][x; y] = [3; 9]
   • [5, -2; 4, 1][x; y] = [3; 9]
3. 3.

   3x + 5y = 13; x + 4y = 2. Number table A = [3, 5; 1, 4]. Pia solves the system in the figure with X = A⁻¹B, where A⁻¹ = (1/7)[4, -5; -1, 3] and B = [13; 2]. What is x?

   6
4. 4.

   Esme replaces row 2 of [1, 3 | 7; 4, 5 | 6] with row 2 − 4 × row 1. What is the new number in row 2, after the bar?

   -22
5. 5.

   Kira replaces row 2 of [1, -2 | 3; 5, 2 | 9] with row 2 − 5 × row 1. What is the new number in row 2, after the bar?

   -6
6. 6.

   Pia solves 2x + 5y = 16 and x + 3y = 10 with X = A⁻¹B. What is y?

   4
7. 7.

   Ren solves 3x + 4y = 5 and 2x + 5y = 8 with X = A⁻¹B. What is x?

   -1
8. 8.

   Tala solves 4x + y = 5 and 3x + 2y = 0 with X = A⁻¹B. What is y?

   -3

9. Read this first

   Start

   [1, 2, -1 | 7; 2, 5, 1 | 24; 1, 5, 9 | 39]. Row steps: row 2 − 2 × row 1, then row 3 − row 1, then row 3 − 3 × row 2.

10. 9.

    Tala row-reduces the system in the figure to the last table [1, 2, -1 | 7; 0, 1, 3 | 10; 0, 0, 1 | 2]. What is y?

    4

11. Start

    [1, 3, 2 | 11; 2, 7, 2 | 15; 5, 16, 9 | 51]. Row steps: row 2 − 2 × row 1, then row 3 − 5 × row 1, then row 3 − row 2.

12. 10.

    Bo row-reduces the system in the figure to the last table [1, 3, 2 | 11; 0, 1, -2 | -7; 0, 0, 1 | 3]. What is x?

    8